Three key differences: 1) The search occurs as you type, so you don't need to specify more of a query than you need to. 2) ST2 searches delineate between searching file names and searching file contents, (with, e.g. "#") and you can combine both in a single query, if you want, to go to a particular location in a particular file. 3) At the end of the search you can hit "Enter" to go to the found file and edit it, or "Esc" to return to where you were before the search (which is great for just poking into another file to check something).

In fact, thinking about it now, they're quite different. The thing that grep excels at can't even be done easily (that I know of) in ST2: "I'm looking for this function called xyz, but I don't remember which file in this directory it's in."